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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment">#</span>
<a name="l00026"></a>00026 
<a name="l00027"></a>00027 <span class="keyword">from</span> scipy <span class="keyword">import</span> c_, r_, diag, tile, dot
<a name="l00028"></a>00028 <span class="keyword">from</span> scipy <span class="keyword">import</span> zeros, linalg
<a name="l00029"></a>00029 <span class="keyword">from</span> numpy <span class="keyword">import</span> sum <span class="keyword">as</span> npsum
<a name="l00030"></a>00030 
<a name="l00031"></a>00031 <span class="keyword">def </span>twod_inner(tria, quad, func):
<a name="l00032"></a>00032     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00033"></a>00033 <span class="stringliteral">    Synopsis:</span>
<a name="l00034"></a>00034 <span class="stringliteral">    --------</span>
<a name="l00035"></a>00035 <span class="stringliteral">      computes the inner product of function f</span>
<a name="l00036"></a>00036 <span class="stringliteral">      against the lagrange function which is one</span>
<a name="l00037"></a>00037 <span class="stringliteral">      on the first node and zero anywhere else.</span>
<a name="l00038"></a>00038 <span class="stringliteral"></span>
<a name="l00039"></a>00039 <span class="stringliteral">   Inputt:</span>
<a name="l00040"></a>00040 <span class="stringliteral">   -----</span>
<a name="l00041"></a>00041 <span class="stringliteral">    tria .- 3x2 array.</span>
<a name="l00042"></a>00042 <span class="stringliteral">    quad .- quadrature formula</span>
<a name="l00043"></a>00043 <span class="stringliteral">    f    .- function</span>
<a name="l00044"></a>00044 <span class="stringliteral">  &quot;&quot;&quot;</span>
<a name="l00045"></a>00045 
<a name="l00046"></a>00046     weights = quad.get_weights()
<a name="l00047"></a>00047     qpoints = quad.get_qpoints()
<a name="l00048"></a>00048     p1_hat = 1.0 - npsum(qpoints, axis=1)
<a name="l00049"></a>00049 
<a name="l00050"></a>00050     amat = r_[tria[1, :] - tria[0, :], tria[2, :] - tria[0, :]]
<a name="l00051"></a>00051     amat = amat.reshape((2, 2))
<a name="l00052"></a>00052     eval_nodes = tile(tria[0, :], (qpoints[:, 0].size, 1))
<a name="l00053"></a>00053     eval_nodes += dot(qpoints, amat.T)
<a name="l00054"></a>00054     funt_at_quads = func(eval_nodes)
<a name="l00055"></a>00055 
<a name="l00056"></a>00056     <span class="keywordflow">return</span> linalg.det(amat) * dot(p1_hat, funt_at_quads * weights) / 2.
<a name="l00057"></a>00057 
<a name="l00058"></a>00058 
<a name="l00059"></a>00059 <span class="keyword">def </span>oned_inner(basis, quad, grid, func, time=0):
<a name="l00060"></a>00060     <span class="stringliteral">&quot;&quot;&quot; compute</span>
<a name="l00061"></a>00061 <span class="stringliteral">        &lt;\phi, f&gt; with respect to the L2 norm.</span>
<a name="l00062"></a>00062 <span class="stringliteral">        \phi are elements of the basis for the finite</span>
<a name="l00063"></a>00063 <span class="stringliteral">        element space</span>
<a name="l00064"></a>00064 <span class="stringliteral">  &quot;&quot;&quot;</span>
<a name="l00065"></a>00065 
<a name="l00066"></a>00066     x_coors = grid.get_grid()
<a name="l00067"></a>00067     delta_x = grid.getDx()
<a name="l00068"></a>00068     nsegs = grid.getNumSegs()
<a name="l00069"></a>00069 
<a name="l00070"></a>00070     qpoints = quad.get_qpoints()
<a name="l00071"></a>00071     poly_at_quads = basis.values(qpoints)
<a name="l00072"></a>00072 
<a name="l00073"></a>00073     weights = quad.get_weights() / 2.
<a name="l00074"></a>00074     poly_at_quads = poly_at_quads * weights.T
<a name="l00075"></a>00075     qpoints = (1.0 + qpoints) / 2.
<a name="l00076"></a>00076 
<a name="l00077"></a>00077     dof = basis.dof()
<a name="l00078"></a>00078     rhs = zeros(((dof - 1) * nsegs + 1, 1))
<a name="l00079"></a>00079     <span class="keywordflow">for</span> (i, delta_xi) <span class="keywordflow">in</span> enumerate(delta_x):
<a name="l00080"></a>00080         func_at_quads = func(qpoints * delta_xi + x_coors[i], time)
<a name="l00081"></a>00081         rhs[(dof - 1) * i:(dof - 1) * i + dof] += delta_xi * dot(poly_at_quads,
<a name="l00082"></a>00082                 func_at_quads)
<a name="l00083"></a>00083 
<a name="l00084"></a>00084     <span class="keywordflow">return</span> rhs
<a name="l00085"></a>00085 
<a name="l00086"></a>00086 
<a name="l00087"></a>00087 <span class="keyword">def </span>ProjOnShapeFunctions(basis, quad, grid, func):
<a name="l00088"></a>00088     <span class="stringliteral">&quot;&quot;&quot; assemble mass matrix &quot;&quot;&quot;</span>
<a name="l00089"></a>00089 
<a name="l00090"></a>00090     delta_x = grid.getDx()
<a name="l00091"></a>00091     nsegs = grid.getNumSegs()
<a name="l00092"></a>00092 
<a name="l00093"></a>00093     mass_matrix = basis.get_mass_mat()
<a name="l00094"></a>00094     dof = basis.dof()
<a name="l00095"></a>00095     diag0 = zeros(((dof - 1) * nsegs + 1, 1))
<a name="l00096"></a>00096 
<a name="l00097"></a>00097     sdiag = diag(mass_matrix)
<a name="l00098"></a>00098     sdiag = sdiag.reshape((dof, 1))
<a name="l00099"></a>00099     <span class="keywordflow">for</span> (i, delta_xi) <span class="keywordflow">in</span> enumerate(delta_x):
<a name="l00100"></a>00100         diag0[(dof - 1) * i:(dof - 1) * i + dof] += sdiag * delta_xi
<a name="l00101"></a>00101 
<a name="l00102"></a>00102     diag0 = diag0.flatten()
<a name="l00103"></a>00103     <span class="keywordflow">if</span> 2 == dof:
<a name="l00104"></a>00104         diag1 = mass_matrix[0, 1] * delta_x.flatten()
<a name="l00105"></a>00105         mass = diag(diag0, 0) + diag(diag1, 1) + diag(diag1, -1)
<a name="l00106"></a>00106 
<a name="l00107"></a>00107     <span class="keywordflow">if</span> 3 == dof:
<a name="l00108"></a>00108         diag1 = (diag(mass_matrix, 1) * c_[delta_x, delta_x]).flatten()
<a name="l00109"></a>00109         diag2 = mass_matrix[0, 2] * c_[delta_x, zeros(delta_x.shape)].flatten()
<a name="l00110"></a>00110         diag2 = diag2[0:-1]
<a name="l00111"></a>00111 
<a name="l00112"></a>00112         mass = diag(diag0) + diag(diag1, 1) + diag(diag1, -1) \
<a name="l00113"></a>00113             + diag(diag2, 2) + diag(diag2, -2)
<a name="l00114"></a>00114 
<a name="l00115"></a>00115     rhs = oned_inner(basis, quad, grid, func)
<a name="l00116"></a>00116     <span class="keywordflow">return</span> linalg.solve(mass, rhs)
<a name="l00117"></a>00117 
<a name="l00118"></a>00118 
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